Definition · Plain-language
Confidence interval
A confidence interval is a range of plausible values for an unknown population parameter, estimated from sample data with a stated level of confidence, such as 95%.
The step most authors miss
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A range, not a single guess
When researchers estimate a quantity such as a population mean or proportion, a single point estimate from a sample is almost never exactly right. A confidence interval surrounds that estimate with a range of plausible values, reflecting sampling uncertainty. A typical result might read "the mean recovery time was 12 days (95% CI: 10 to 14 days)". The interval’s width depends on the variability in the data, the sample size and the chosen confidence level: larger samples and less variable data yield narrower, more precise intervals.
What the confidence level really means
The confidence level describes the long-run performance of the procedure, not a single interval. A 95% confidence level means that if you repeated the whole study many times, drawing fresh samples and computing an interval each time, about 95% of those intervals would contain the true parameter. The 95% is a property of the method across hypothetical repetitions. For any one interval already calculated, the true value is either inside it or not — there is no probability attached to that specific interval under the standard frequentist view.
The common misinterpretation
The most frequent error is to read a 95% confidence interval as "there is a 95% probability the true value lies in this interval". That statement is incorrect in frequentist statistics: the parameter is fixed, and the interval either captures it or it does not. The 95% refers to the reliability of the method over many samples, not the probability for the one interval in front of you. A confidence interval also complements a p-value — if a 95% interval for a difference excludes zero, the result is significant at the 0.05 level.
Key facts
At a glance
- Definition: a range of plausible values for a population parameter
- Confidence level: e.g. 95% — a property of the method over repeated sampling
- Interpretation: ~95% of such intervals would contain the true value
- Width: narrower with larger samples and less variable data
- Link to testing: a 95% CI excluding the null value implies p < 0.05
- Common error: reading 95% as the probability for one specific interval
Common misconceptions
What people often get wrong
Often heard: A 95% confidence interval means there is a 95% probability the true value lies in this particular interval.
Actually: No. The parameter is fixed; a given interval either contains it or not. The 95% describes the method: across many repeated samples, about 95% of the intervals produced would capture the true value.
Often heard: A confidence interval shows the range in which 95% of the data lie.
Actually: It does not. A confidence interval estimates a population parameter such as the mean, not the spread of individual data points. The range covering most data values is a prediction or tolerance interval instead.
Often heard: A wider confidence interval is always worse.
Actually: Not inherently. A wider interval reflects greater uncertainty, usually from a smaller sample or more variable data, but it is an honest expression of that uncertainty. A misleadingly narrow interval from a flawed method is far worse.
Going deeper
